Most engineering applications, in a wide range of domains, are based on mathematically founded methods and algorithms. This excellent introductory textbook covers numerical methods that are currently used to model and solve engineering problems.

The first two chapters focus on the basic concepts used in scientific computing, such as error analysis and algorithmic approaches. The next two chapters present a series of standard techniques in solving equations and the optimization of functions in one variable; a brief review of concepts and results from linear algebra follows. Chapter 5 covers linear systems and presents the Gaussian elimination method, LU and Cholesky decompositions, and permutations and ordering strategies. Of particular value are the comments and solutions concerning implementation and estimation of errors and the condition number.

The next three chapters focus on the use of the linear least squares paradigm, iterative methods in solving linear systems, and methods that involve the computation of eigenvalues and singular value decomposition. Nonlinear optimization problems arise frequently in engineering problems and require refined mathematical treatment and numerical solutions. The fundamentals of nonlinear systems and nonlinear optimization are provided in chapter 9, where, besides Newton’s method, unconstrained and constrained optimization methods and their MATLAB codes are presented and illustrated with numerical examples.

Some polynomial interpolation and piecewise polynomial interpolation methods are provided in the next three chapters, followed by approximation and decomposition schemes based on trigonometric polynomials, Fourier, and the fast Fourier transform method. In chapter 13, discrete cosine transforms are presented. The next two chapters examine numerical differentiation and integration methods; standard, classical techniques are presented, along with a series of interesting comments concerning their use in signal processing applications. The final chapter concentrates on developing methods and concepts for solving ordinary differential equations, with the discussion centering mainly on the problem of solving initial value problems.

The list of bibliographic references contains a significant number of the most relevant published papers and books in the numerical algorithms area.

The book proves extremely useful to a large class of readers, including engineers and scientists who want to implement solutions to numerical tasks in MATLAB or another programming language and students in computer science, engineering, and mathematics departments. Moreover, given its remarkable pedagogical features, I believe that the book can be successfully used as a handbook in teaching courses involving the use of numerical methods.